Compare Decimals: Finding the Correct Symbol Between 0.3 and 0.30

Q: Why does 0.3 equal 0.30 when they look different?

Both numbers represent 3 tenths! Adding zeros after the last digit doesn't change the value, just like writing 7 or 007 - they're the same number.

Q: How can I tell if two decimals are equal?

Make them have the same number of decimal places by adding zeros, then compare digit by digit from left to right. If all digits match, they're equal!

Q: Does 0.30 have more value than 0.3 because it's more precise?

No! Mathematical value stays the same. The extra zero might show precision in measurement, but for pure math comparison, $ 0.3 = 0.30 $.

Q: Can I remove trailing zeros from any decimal?

Yes! You can always remove trailing zeros after the decimal point without changing the value. 0.500 = 0.50 = 0.5 - they're all equal.

Decimal Comparison with Trailing Zeros

Fill in the missing sign:

$0.3\text{ }_{—\text{ }}0.30$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose the appropriate sign

00:03 Let's compare the digits between the numbers

00:07 You can always add more 0s on the right side after the decimal point

00:09 We can see that the numbers are equal

00:13 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Fill in the missing sign:

$0.3\text{ }_{—\text{ }}0.30$

Step-by-step solution

In order to compare which is greater, we will compare the numbers by adding 0 to 0.3 in the following way:

$0.30\text{?}0.30$

Note that before the decimal point we have 0 in both numbers

After the decimal point in both numbers we have the number 3 and then the number 0

Therefore, the appropriate sign is:

$0.30=0.30$

Final Answer

$=$

Key Points to Remember

Essential concepts to master this topic

Rule: Trailing zeros after decimal point don't change value
Technique: Add zeros to match decimal places: 0.3 = 0.30
Check: Convert both to same form and compare digit by digit ✓

Common Mistakes

Avoid these frequent errors

Thinking more digits means larger number
Don't assume 0.30 > 0.3 because it has more digits = wrong comparison! More decimal places doesn't mean greater value when they're just trailing zeros. Always remember that trailing zeros don't change the decimal's value.

Practice Quiz

Test your knowledge with interactive questions

Reduce the following fraction:

$$ 0.30 $$

FAQ

Everything you need to know about this question

Why does 0.3 equal 0.30 when they look different?

Both numbers represent 3 tenths! Adding zeros after the last digit doesn't change the value, just like writing 7 or 007 - they're the same number.

How can I tell if two decimals are equal?

Make them have the same number of decimal places by adding zeros, then compare digit by digit from left to right. If all digits match, they're equal!

Does 0.30 have more value than 0.3 because it's more precise?

No! Mathematical value stays the same. The extra zero might show precision in measurement, but for pure math comparison, $0.3 = 0.30$ .

What's the easiest way to compare decimals like these?

Line them up by decimal point and add zeros to make equal lengths:

0.30
0.30

Now compare - they're identical!

Can I remove trailing zeros from any decimal?

Yes! You can always remove trailing zeros after the decimal point without changing the value. 0.500 = 0.50 = 0.5 - they're all equal.

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